The chemical and nuclear properties of the nucleus are determined by the number of protons, called the atomic number, and the number of neutrons, called the neutron number. The atomic mass number is the total number of nucleons. For example, carbon has atomic number 6, and its abundant carbon-12 isotope has 6 neutrons, whereas its rare carbon-13 isotope has 7 neutrons. Some elements occur in nature with only one stable isotope, such as fluorine. Other elements occur with many stable isotopes, such as tin with ten stable isotopes.

Within the nucleus, protons and neutrons are bound together through the nuclear force. Neutrons are required for the stability of nuclei, with the exception of the single-proton hydrogen atom. Neutrons are produced copiously in nuclear fission and fusion. They are a primary contributor to the nucleosynthesis of chemical elements within stars through fission, fusion, and neutron capture processes.

An atomic nucleus is formed by a number of protons, Z (the atomic number), and a number of neutrons, N (the neutron number), bound together by the nuclear force. The atomic number defines the chemical properties of the atom, and the neutron number determines the isotope or nuclide.[8] The terms isotope and nuclide are often used synonymously, but they refer to chemical and nuclear properties, respectively. Strictly speaking, isotopes are two or more nuclides with the same number of protons; nuclides with the same number of neutrons are called isotones. The atomic mass number, symbol A, equals Z+N. Nuclides with the same atomic mass number are called isobars. The nucleus of the most common isotope of the hydrogen atom (with the chemical symbol1H) is a lone proton. The nuclei of the heavy hydrogen isotopes deuterium (D or 2H) and tritium (T or 3H) contain one proton bound to one and two neutrons, respectively. All other types of atomic nuclei are composed of two or more protons and various numbers of neutrons. The most common nuclide of the common chemical element lead, 208Pb, has 82 protons and 126 neutrons, for example. The table of nuclides comprises all the known nuclides. Even though it is not a chemical element, the neutron is included in this table.[10]

The free neutron has a mass of 939,565,413.3 eV/c2, or 1.674927471×10−27kg, or 1.00866491588u.[3] The neutron has a mean square radius of about 0.8×10−15m, or 0.8 fm,[11] and it is a spin-½fermion.[12]
The neutron has no measurable electric charge. With its positive electric charge, the proton is directly influenced by electric fields, whereas the neutron is unaffected by electric fields. The neutron has a magnetic moment, however, so the neutron is influenced by magnetic fields. The neutron's magnetic moment has a negative value, because its orientation is opposite to the neutron's spin.[13]

A free neutron is unstable, decaying to a proton, electron and antineutrino with a mean lifetime of just under 15 minutes (881.5±1.5 s).[14] This radioactive decay, known as beta decay, is possible because the mass of the neutron is slightly greater than the proton. The free proton is stable. Neutrons or protons bound in a nucleus can be stable or unstable, however, depending on the nuclide. Beta decay, in which neutrons decay to protons, or vice versa, is governed by the weak force, and it requires the emission or absorption of electrons and neutrinos, or their antiparticles.

Nuclear fission caused by absorption of a neutron by uranium-235. The heavy nuclide fragments into lighter components and additional neutrons.

Protons and neutrons behave almost identically under the influence of the nuclear force within the nucleus. The concept of isospin, in which the proton and neutron are viewed as two quantum states of the same particle, is used to model the interactions of nucleons by the nuclear or weak forces. Because of the strength of the nuclear force at short distances, the binding energy of nucleons is more than seven orders of magnitude larger than the electromagnetic energy binding electrons in atoms. Nuclear reactions (such as nuclear fission) therefore have an energy density that is more than ten million times that of chemical reactions. Because of the mass–energy equivalence, nuclear binding energies reduce the mass of nuclei. Ultimately, the ability of the nuclear force to store energy arising from the electromagnetic repulsion of nuclear components is the basis for most of the energy that makes nuclear reactors or bombs possible. In nuclear fission, the absorption of a neutron by a heavy nuclide (e.g., uranium-235) causes the nuclide to become unstable and break into light nuclides and additional neutrons. The positively charged light nuclides then repel, releasing electromagnetic potential energy.

The story of the discovery of the neutron and its properties is central to the extraordinary developments in atomic physics that occurred in the first half of the 20th century, leading ultimately to the atomic bomb in 1945. In the 1911 Rutherford model, the atom consisted of a small positively charged massive nucleus surrounded by a much larger cloud of negatively charged electrons. In 1920, Rutherford suggested that the nucleus consisted of positive protons and neutrally-charged particles, suggested to be a proton and an electron bound in some way.[17] Electrons were assumed to reside within the nucleus because it was known that beta radiation consisted of electrons emitted from the nucleus.[17] Rutherford called these uncharged particles neutrons, by the Latin root for neutralis (neuter) and the Greek suffix -on (a suffix used in the names of subatomic particles, i.e. electron and proton).[18][19] References to the word neutron in connection with the atom can be found in the literature as early as 1899, however.[20]

Throughout the 1920s, physicists assumed that the atomic nucleus was composed of protons and "nuclear electrons"[21][22] but there were obvious problems. It was difficult to reconcile the proton–electron model for nuclei with the Heisenberg uncertainty relation of quantum mechanics.[23][24] The Klein paradox,[25] discovered by Oskar Klein in 1928, presented further quantum mechanical objections to the notion of an electron confined within a nucleus.[23] Observed properties of atoms and molecules were inconsistent with the nuclear spin expected from the proton–electron hypothesis. Both protons and electrons carry an intrinsic spin of ½ ħ. Isotopes of the same species (i.e having the same number of protons) can have both integer or fractional spin, i.e. the neutron spin must be also fractional (½ ħ). However, there is no way to arrange the spins of an electron and a proton (supposed to bond to form a neutron) to get the fractional spin of a neutron.

Models depicting the nucleus and electron energy levels in hydrogen, helium, lithium, and neon atoms. In reality, the diameter of the nucleus is about 100,000 times smaller than the diameter of the atom.

Models for atomic nucleus consisting of protons and neutrons were quickly developed by Werner Heisenberg[32][33][34] and others.[35][36] The proton–neutron model explained the puzzle of nuclear spins. The origins of beta radiation were explained by Enrico Fermi in 1934 by the process of beta decay, in which the neutron decays to a proton by creating an electron and a (as yet undiscovered) neutrino.[37] In 1935 Chadwick and his doctoral student Maurice Goldhaber, reported the first accurate measurement of the mass of the neutron.[38][39]

By 1934, Fermi had bombarded heavier elements with neutrons to induce radioactivity in elements of high atomic number. In 1938, Fermi received the Nobel Prize in Physics "for his demonstrations of the existence of new radioactive elements produced by neutron irradiation, and for his related discovery of nuclear reactions brought about by slow neutrons".[40] In 1938 Otto Hahn, Lise Meitner, and Fritz Strassmann discovered nuclear fission, or the fractionation of uranium nuclei into light elements, induced by neutron bombardment.[41][42][43] In 1945 Hahn received the 1944 Nobel Prize in Chemistry"for his discovery of the fission of heavy atomic nuclei."[44][45][46] The discovery of nuclear fission would lead to the development of nuclear power and the atomic bomb by the end of World War II.

Outside the nucleus, free neutrons are unstable and have a mean lifetime of 881.5±1.5 s (about 14 minutes, 42 seconds); therefore the half-life for this process (which differs from the mean lifetime by a factor of ln(2) = 0.693) is 611.0±1.0 s (about 10 minutes, 11 seconds).[14] Beta decay of the neutron, described above, can be denoted by the radioactive decay:[48]

n0 → p+ + e− + νe

where p+, e−, and νe denote the proton, electron and electron antineutrino, respectively.
For the free neutron the decay energy for this process (based on the masses of the neutron, proton, and electron) is 0.782343 MeV. The maximal energy of the beta decay electron (in the process wherein the neutrino receives a vanishingly small amount of kinetic energy) has been measured at 0.782 ± 0.013 MeV.[49] The latter number is not well-enough measured to determine the comparatively tiny rest mass of the neutrino (which must in theory be subtracted from the maximal electron kinetic energy) as well as neutrino mass is constrained by many other methods.

A small fraction (about one in 1000) of free neutrons decay with the same products, but add an extra particle in the form of an emitted gamma ray:

n0 → p+ + e− + νe + γ

This gamma ray may be thought of as an "internal bremsstrahlung" that arises from the electromagnetic interaction of the emitted beta particle with the proton. Internal bremsstrahlung gamma ray production is also a minor feature of beta decays of bound neutrons (as discussed below).

A schematic of the nucleus of an atom indicating β− radiation, the emission of a fast electron from the nucleus (the accompanying antineutrino is omitted). In the Rutherford model for the nucleus, red spheres were protons with positive charge and blue spheres were protons tightly bound to an electron with no net charge. The inset shows beta decay of a free neutron as it is understood today; an electron and antineutrino are created in this process.

A very small minority of neutron decays (about four per million) are so-called "two-body (neutron) decays", in which a proton, electron and antineutrino are produced as usual, but the electron fails to gain the 13.6 eV necessary energy to escape the proton (the ionization energy of hydrogen), and therefore simply remains bound to it, as a neutral hydrogen atom (one of the "two bodies"). In this type of free neutron decay, almost all of the neutron decay energy is carried off by the antineutrino (the other "body"). (The hydrogen atom recoils with a speed of only about (decay energy)/(hydrogen rest energy) times the speed of light, or 250 km/s.)

The transformation of a free proton to a neutron (plus a positron and a neutrino) is energetically impossible, since a free neutron has a greater mass than a free proton. But a high-energy collision of a proton and an electron or neutrino can result in a neutron.

While a free neutron has a half life of about 10.2 min, most neutrons within nuclei are stable. According to the nuclear shell model, the protons and neutrons of a nuclide are a quantum mechanical system organized into discrete energy levels with unique quantum numbers. For a neutron to decay, the resulting proton requires an available state at lower energy than the initial neutron state. In stable nuclei the possible lower energy states are all filled, meaning they are each occupied by two protons with spin up and spin down. The Pauli exclusion principle therefore disallows the decay of a neutron to a proton within stable nuclei. The situation is similar to electrons of an atom, where electrons have distinct atomic orbitals and are prevented from decaying to lower energy states, with the emission of a photon, by the exclusion principle.

Neutrons in unstable nuclei can decay by beta decay as described above. In this case, an energetically allowed quantum state is available for the proton resulting from the decay. One example of this decay is carbon-14 (6 protons, 8 neutrons) that decays to nitrogen-14 (7 protons, 7 neutrons) with a half-life of about 5,730 years.

Inside a nucleus, a proton can transform into a neutron via inverse beta decay, if an energetically allowed quantum state is available for the neutron. This transformation occurs by emission of a positron and an electron neutrino:

p+ → n0 + e+ + νe

The transformation of a proton to a neutron inside of a nucleus is also possible through electron capture:

p+ + e− → n0 + νe

Positron capture by neutrons in nuclei that contain an excess of neutrons is also possible, but is hindered because positrons are repelled by the positive nucleus, and quickly annihilate when they encounter electrons.

Three types of beta decay in competition are illustrated by the single isotope copper-64 (29 protons, 35 neutrons), which has a half-life of about 12.7 hours. This isotope has one unpaired proton and one unpaired neutron, so either the proton or the neutron can decay. This particular nuclide is almost equally likely to undergo proton decay (by positron emission, 18% or by electron capture, 43%) or neutron decay (by electron emission, 39%).

The mass of a neutron cannot be directly determined by mass spectrometry due to lack of electric charge. However, since the masses of a proton and of a deuteron can be measured with a mass spectrometer, the mass of a neutron can be deduced by subtracting proton mass from deuteron mass, with the difference being the mass of the neutron plus the binding energy of deuterium (expressed as a positive emitted energy). The latter can be directly measured by measuring the energy (Bd{\displaystyle B_{d}}) of the single 0.7822 MeV gamma photon emitted when neutrons are captured by protons (this is exothermic and happens with zero-energy neutrons), plus the small recoil kinetic energy (Erd{\displaystyle E_{rd}}) of the deuteron (about 0.06% of the total energy).

mn=md−mp+Bd−Erd{\displaystyle m_{n}=m_{d}-m_{p}+B_{d}-E_{rd}}

The energy of the gamma ray can be measured to high precision by X-ray diffraction techniques, as was first done by Bell and Elliot in 1948. The best modern (1986) values for neutron mass by this technique are provided by Greene, et al.[50] These give a neutron mass of:

The total electric charge of the neutron is 0 e. This zero value has been tested experimentally, and the present experimental limit for the charge of the neutron is −2(8)×10−22e,[4] or −3(13)×10−41C. This value is consistent with zero, given the experimental uncertainties (indicated in parentheses). By comparison, the charge of the proton is +1 e.

Even though the neutron is a neutral particle, the magnetic moment of a neutron is not zero. The neutron is not affected by electric fields, but it is affected by magnetic fields. The magnetic moment of the neutron is an indication of its quark substructure and internal charge distribution.[52]
The value for the neutron's magnetic moment was first directly measured by Luis Alvarez and Felix Bloch at Berkeley, California, in 1940.[53] Alvarez and Bloch determined the magnetic moment of the neutron to be μn= −1.93(2) μN, where μN is the nuclear magneton.

In the quark model for hadrons, the neutron is composed of one up quark (charge +2/3 e) and two down quarks (charge −1/3 e).[52] The magnetic moment of the neutron can be modeled as a sum of the magnetic moments of the constituent quarks.[54] The calculation assumes that the quarks behave like pointlike Dirac particles, each having their own magnetic moment. Simplistically, the magnetic moment of the neutron can be viewed as resulting from the vector sum of the three quark magnetic moments, plus the orbital magnetic moments caused by the movement of the three charged quarks within the neutron.

The above treatment compares neutrons with protons, allowing the complex behavior of quarks to be subtracted out between models, and merely exploring what the effects would be of differing quark charges (or quark type). Such calculations are enough to show that the interior of neutrons is very much like that of protons, save for the difference in quark composition with a down quark in the neutron replacing an up quark in the proton.

The neutron magnetic moment can be roughly computed by assuming a simple nonrelativistic, quantum mechanical wavefunction for baryons composed of three quarks. A straightforward calculation gives fairly accurate estimates for the magnetic moments of neutrons, protons, and other baryons.[54] For a neutron, the end result of this calculation is that the magnetic moment of the neutron is given by μn= 4/3 μd − 1/3 μu, where μd and μu are the magnetic moments for the down and up quarks, respectively. This result combines the intrinsic magnetic moments of the quarks with their orbital magnetic moments, and assumes the three quarks are in a particular, dominant quantum state.

Baryon

Magnetic momentof quark model

Computed(μN{\displaystyle \mu _{\mathrm {N} }})

Observed(μN{\displaystyle \mu _{\mathrm {N} }})

p

4/3 μu − 1/3 μd

2.79

2.793

n

4/3 μd − 1/3 μu

−1.86

−1.913

The results of this calculation are encouraging, but the masses of the up or down quarks were assumed to be 1/3 the mass of a nucleon.[54] The masses of the quarks are actually only about 1% that of a nucleon.[58] The discrepancy stems from the complexity of the Standard Model for nucleons, where most of their mass originates in the gluon fields, virtual particles, and their associated energy that are essential aspects of the strong force.[58][59] Furthermore, the complex system of quarks and gluons that constitute a neutron requires a relativistic treatment.[60] The nucleon magnetic moment has been successfully computed numerically from first principles, however, including all the effects mentioned and using more realistic values for the quark masses. The calculation gave results that were in fair agreement with measurement, but it required significant computing resources.[61][62]

The neutron is a spin 1/2 particle, that is, it is a fermion with intrinsic angular momentum equal to 1/2 ħ, where ħ is the reduced Planck constant. For many years after the discovery of the neutron, its exact spin was ambiguous. Although it was assumed to be a spin 1/2 Dirac particle, the possibility that the neutron was a spin 3/2 particle lingered. The interactions of the neutron's magnetic moment with an external magnetic field were exploited to finally determine the spin of the neutron.[63] In 1949, Hughes and Burgy measured neutrons reflected from a ferromagnetic mirror and found that the angular distribution of the reflections was consistent with spin 1/2.[64] In 1954, Sherwood, Stephenson, and Bernstein employed neutrons in a Stern–Gerlach experiment that used a magnetic field to separate the neutron spin states. They recorded two such spin states, consistent with a spin 1/2 particle.[63][65]

An article published in 2007 featuring a model-independent analysis concluded that the neutron has a negatively charged exterior, a positively charged middle, and a negative core.[66] In a simplified classical view, the negative "skin" of the neutron assists it to be attracted to the protons with which it interacts in the nucleus. (However, the main attraction between neutrons and protons is via the nuclear force, which does not involve electric charge.)

The simplified classical view of the neutron's charge distribution also "explains" the fact that the neutron magnetic dipole points in the opposite direction from its spin angular momentum vector (as compared to the proton). This gives the neutron, in effect, a magnetic moment which resembles a negatively charged particle. This can be reconciled classically with a neutral neutron composed of a charge distribution in which the negative sub-parts of the neutron have a larger average radius of distribution, and therefore contribute more to the particle's magnetic dipole moment, than do the positive parts that are, on average, nearer the core.

The Standard Model of particle physics predicts a tiny separation of positive and negative charge within the neutron leading to a permanent electric dipole moment.[67] The predicted value is, however, well below the current sensitivity of experiments. From several unsolved puzzles in particle physics, it is clear that the Standard Model is not the final and full description of all particles and their interactions. New theories going beyond the Standard Model generally lead to much larger predictions for the electric dipole moment of the neutron. Currently, there are at least four experiments trying to measure for the first time a finite neutron electric dipole moment, including:

The antineutron is the antiparticle of the neutron. It was discovered by Bruce Cork in 1956, a year after the antiproton was discovered. CPT-symmetry puts strong constraints on the relative properties of particles and antiparticles, so studying antineutrons provides stringent tests on CPT-symmetry. The fractional difference in the masses of the neutron and antineutron is (9±6)×10−5. Since the difference is only about two standard deviations away from zero, this does not give any convincing evidence of CPT-violation.[14]

The existence of stable clusters of 4 neutrons, or tetraneutrons, has been hypothesised by a team led by Francisco-Miguel Marqués at the CNRS Laboratory for Nuclear Physics based on observations of the disintegration of beryllium-14 nuclei. This is particularly interesting because current theory suggests that these clusters should not be stable.

In February 2016, Japanese physicist Susumu Shimoura of the University of Tokyo and co-workers reported they had observed the purported tetraneutrons for the first time experimentally.[73] Nuclear physicists around the world say this discovery, if confirmed, would be a milestone in the field of nuclear physics and certainly would deepen our understanding of the nuclear forces.[74][75]

The dineutron is another hypothetical particle. In 2012, Artemis Spyrou from Michigan State University and coworkers reported that they observed, for the first time, the dineutron emission in the decay of 16Be. The dineutron character is evidenced by a small emission angle between the two neutrons. The authors measured the two-neutron separation energy to be 1.35(10) MeV, in good agreement with shell model calculations, using standard interactions for this mass region.[76]

The common means of detecting a chargedparticle by looking for a track of ionization (such as in a cloud chamber) does not work for neutrons directly. Neutrons that elastically scatter off atoms can create an ionization track that is detectable, but the experiments are not as simple to carry out; other means for detecting neutrons, consisting of allowing them to interact with atomic nuclei, are more commonly used. The commonly used methods to detect neutrons can therefore be categorized according to the nuclear processes relied upon, mainly neutron capture or elastic scattering.[78]

A common method for detecting neutrons involves converting the energy released from neutron capture reactions into electrical signals. Certain nuclides have a high neutron capture cross section, which is the probability of absorbing a neutron. Upon neutron capture, the compound nucleus emits more easily detectable radiation, for example an alpha particle, which is then detected. The nuclides 3He, 6Li, 10B, 233U, 235U, 237Np, and 239Pu are useful for this purpose.

Neutrons can elastically scatter off nuclei, causing the struck nucleus to recoil. Kinematically, a neutron can transfer more energy to a light nucleus such as hydrogen or helium than to a heavier nucleus. Detectors relying on elastic scattering are called fast neutron detectors. Recoiling nuclei can ionize and excite further atoms through collisions. Charge and/or scintillation light produced in this way can be collected to produce a detected signal. A major challenge in fast neutron detection is discerning such signals from erroneous signals produced by gamma radiation in the same detector.

Fast neutron detectors have the advantage of not requiring a moderator, and are therefore capable of measuring the neutron's energy, time of arrival, and in certain cases direction of incidence.

Free neutrons are unstable, although they have the longest half-life of any unstable subatomic particle by several orders of magnitude. Their half-life is still only about 10 minutes, however, so they can be obtained only from sources that produce them continuously.

Natural neutron background. A small natural background flux of free neutrons exists everywhere on Earth. In the atmosphere and deep into the ocean, the "neutron background" is caused by muons produced by cosmic ray interaction with the atmosphere. These high-energy muons are capable of penetration to considerable depths in water and soil. There, in striking atomic nuclei, among other reactions they induce spallation reactions in which a neutron is liberated from the nucleus. Within the Earth's crust a second source is neutrons produced primarily by spontaneous fission of uranium and thorium present in crustal minerals. The neutron background is not strong enough to be a biological hazard, but it is of importance to very high resolution particle detectors that are looking for very rare events, such as (hypothesized) interactions that might be caused by particles of dark matter.[9] Recent research has shown that even thunderstorms can produce neutrons with energies of up to several tens of MeV.[79] Recent research has shown that the fluence of these neutrons lies between 10−9 and 10−13 per ms and per m2 depending on the detection altitude. The energy of most of these neutrons, even with initial energies of 20 MeV, decreases down to the keV range within 1 ms.[80]

Even stronger neutron background radiation is produced at the surface of Mars, where the atmosphere is thick enough to generate neutrons from cosmic ray muon production and neutron-spallation, but not thick enough to provide significant protection from the neutrons produced. These neutrons not only produce a Martian surface neutron radiation hazard from direct downward-going neutron radiation but may also produce a significant hazard from reflection of neutrons from the Martian surface, which will produce reflected neutron radiation penetrating upward into a Martian craft or habitat from the floor.[81]

Sources of neutrons for research. These include certain types of radioactive decay (spontaneous fission and neutron emission), and from certain nuclear reactions. Convenient nuclear reactions include tabletop reactions such as natural alpha and gamma bombardment of certain nuclides, often beryllium or deuterium, and induced nuclear fission, such as occurs in nuclear reactors. In addition, high-energy nuclear reactions (such as occur in cosmic radiation showers or accelerator collisions) also produce neutrons from disintegration of target nuclei. Small (tabletop) particle accelerators optimized to produce free neutrons in this way, are called neutron generators.

In practice, the most commonly used small laboratory sources of neutrons use radioactive decay to power neutron production. One noted neutron-producing radioisotope, californium-252 decays (half-life 2.65 years) by spontaneous fission 3% of the time with production of 3.7 neutrons per fission, and is used alone as a neutron source from this process. Nuclear reaction sources (that involve two materials) powered by radioisotopes use an alpha decay source plus a beryllium target, or else a source of high-energy gamma radiation from a source that undergoes beta decay followed by gamma decay, which produces photoneutrons on interaction of the high-energy gamma ray with ordinary stable beryllium, or else with the deuterium in heavy water. A popular source of the latter type is radioactive antimony-124 plus beryllium, a system with a half-life of 60.9 days, which can be constructed from natural antimony (which is 42.8% stable antimony-123) by activating it with neutrons in a nuclear reactor, then transported to where the neutron source is needed.[82]

Experimental nuclear fusion reactors produce free neutrons as a waste product. However, it is these neutrons that possess most of the energy, and converting that energy to a useful form has proved a difficult engineering challenge. Fusion reactors that generate neutrons are likely to create radioactive waste, but the waste is composed of neutron-activated lighter isotopes, which have relatively short (50–100 years) decay periods as compared to typical half-lives of 10,000 years[citation needed] for fission waste, which is long due primarily to the long half-life of alpha-emitting transuranic actinides.[83]

The neutron's lack of total electric charge makes it difficult to steer or accelerate them. Charged particles can be accelerated, decelerated, or deflected by electric or magnetic fields. These methods have little effect on neutrons. However, some effects may be attained by use of inhomogeneous magnetic fields because of the neutron's magnetic moment. Neutrons can be controlled by methods that include moderation, reflection, and velocity selection. Thermal neutrons can be polarized by transmission through magnetic materials in a method analogous to the Faraday effect for photons. Cold neutrons of wavelengths of 6–7 angstroms can be produced in beams of a high degree of polarization, by use of magnetic mirrors and magnetized interference filters.[84]

The development of "neutron lenses" based on total internal reflection within hollow glass capillary tubes or by reflection from dimpled aluminum plates has driven ongoing research into neutron microscopy and neutron/gamma ray tomography.[85][86][87]

Another use of neutron emitters is the detection of light nuclei, in particular the hydrogen found in water molecules. When a fast neutron collides with a light nucleus, it loses a large fraction of its energy. By measuring the rate at which slow neutrons return to the probe after reflecting off of hydrogen nuclei, a neutron probe may determine the water content in soil.

Because neutron radiation is both penetrating and ionizing, it can be exploited for medical treatments. Neutron radiation can have the unfortunate side-effect of leaving the affected area radioactive, however. Neutron tomography is therefore not a viable medical application.

Fast neutron therapy utilizes high-energy neutrons typically greater than 20 MeV to treat cancer. Radiation therapy of cancers is based upon the biological response of cells to ionizing radiation. If radiation is delivered in small sessions to damage cancerous areas, normal tissue will have time to repair itself, while tumor cells often cannot.[88] Neutron radiation can deliver energy to a cancerous region at a rate an order of magnitude larger than gamma radiation.[89]

Beams of low-energy neutrons are used in boron capture therapy to treat cancer. In boron capture therapy, the patient is given a drug that contains boron and that preferentially accumulates in the tumor to be targeted. The tumor is then bombarded with very low-energy neutrons (although often higher than thermal energy) which are captured by the boron-10 isotope in the boron, which produces an excited state of boron-11 that then decays to produce lithium-7 and an alpha particle that have sufficient energy to kill the malignant cell, but insufficient range to damage nearby cells. For such a therapy to be applied to the treatment of cancer, a neutron source having an intensity of the order of a thousand million (109) neutrons per second per cm2 is preferred. Such fluxes require a research nuclear reactor.

Exposure to free neutrons can be hazardous, since the interaction of neutrons with molecules in the body can cause disruption to molecules and atoms, and can also cause reactions that give rise to other forms of radiation (such as protons). The normal precautions of radiation protection apply: Avoid exposure, stay as far from the source as possible, and keep exposure time to a minimum. Some particular thought must be given to how to protect from neutron exposure, however. For other types of radiation, e.g., alpha particles, beta particles, or gamma rays, material of a high atomic number and with high density make for good shielding; frequently, lead is used. However, this approach will not work with neutrons, since the absorption of neutrons does not increase straightforwardly with atomic number, as it does with alpha, beta, and gamma radiation. Instead one needs to look at the particular interactions neutrons have with matter (see the section on detection above). For example, hydrogen-rich materials are often used to shield against neutrons, since ordinary hydrogen both scatters and slows neutrons. This often means that simple concrete blocks or even paraffin-loaded plastic blocks afford better protection from neutrons than do far more dense materials. After slowing, neutrons may then be absorbed with an isotope that has high affinity for slow neutrons without causing secondary capture radiation, such as lithium-6.

Thermal neutrons are free neutrons whose energies have a Maxwell–Boltzmann distribution with kT= 0.0253 eV (4.0×10−21J) at room temperature. This gives characteristic (not average, or median) speed of 2.2 km/s. The name 'thermal' comes from their energy being that of the room temperature gas or material they are permeating. (see kinetic theory for energies and speeds of molecules). After a number of collisions (often in the range of 10–20) with nuclei, neutrons arrive at this energy level, provided that they are not absorbed.

In many substances, thermal neutron reactions show a much larger effective cross-section than reactions involving faster neutrons, and thermal neutrons can therefore be absorbed more readily (i.e., with higher probability) by any atomic nuclei that they collide with, creating a heavier – and often unstable – isotope of the chemical element as a result.

Cold neutrons are thermal neutrons that have been equilibrated in a very cold substance such as liquid deuterium. Such a cold source is placed in the moderator of a research reactor or spallation source. Cold neutrons are particularly valuable for neutron scattering experiments.[citation needed]

Cold neutron source providing neutrons at about the temperature of liquid hydrogen

Ultracold neutrons are produced by elastically scattering cold neutrons in substances with a temperature of a few kelvins, such as solid deuterium or superfluid helium. An alternative production method is the mechanical deceleration of cold neutrons.

A fast neutron is a free neutron with a kinetic energy level close to 1 MeV (1.6×10−13J), hence a speed of ~14000 km/s (~ 5% of the speed of light). They are named fission energy or fast neutrons to distinguish them from lower-energy thermal neutrons, and high-energy neutrons produced in cosmic showers or accelerators. Fast neutrons are produced by nuclear processes such as nuclear fission. Neutrons produced in fission, as noted above, have a Maxwell–Boltzmann distribution of kinetic energies from 0 to ~14 MeV, a mean energy of 2 MeV (for U-235 fission neutrons), and a mode of only 0.75 MeV, which means that more than half of them do not qualify as fast (and thus have almost no chance of initiating fission in fertile materials, such as U-238 and Th-232).

The fusion reaction rate increases rapidly with temperature until it maximizes and then gradually drops off. The DT rate peaks at a lower temperature (about 70 keV, or 800 million kelvins) and at a higher value than other reactions commonly considered for fusion energy.

D–T (deuterium–tritium) fusion is the fusion reaction that produces the most energetic neutrons, with 14.1 MeV of kinetic energy and traveling at 17% of the speed of light. D–T fusion is also the easiest fusion reaction to ignite, reaching near-peak rates even when the deuterium and tritium nuclei have only a thousandth as much kinetic energy as the 14.1 MeV that will be produced.

14.1 MeV neutrons have about 10 times as much energy as fission neutrons, and are very effective at fissioning even non-fissileheavy nuclei, and these high-energy fissions produce more neutrons on average than fissions by lower-energy neutrons. This makes D–T fusion neutron sources such as proposed tokamak power reactors useful for transmutation of transuranic waste. 14.1 MeV neutrons can also produce neutrons by knocking them loose from nuclei.

Other fusion reactions produce much less energetic neutrons. D–D fusion produces a 2.45 MeV neutron and helium-3 half of the time, and produces tritium and a proton but no neutron the rest of the time. D–3He fusion produces no neutron.

A fission energy neutron that has slowed down but not yet reached thermal energies is called an epithermal neutron.

Cross sections for both capture and fission reactions often have multiple resonance peaks at specific energies in the epithermal energy range.
These are of less significance in a fast neutron reactor, where most neutrons are absorbed before slowing down to this range, or in a well-moderatedthermal reactor, where epithermal neutrons interact mostly with moderator nuclei, not with either fissile or fertileactinide nuclides.
However, in a partially moderated reactor with more interactions of epithermal neutrons with heavy metal nuclei, there are greater possibilities for transient changes in reactivity that might make reactor control more difficult.

Ratios of capture reactions to fission reactions are also worse (more captures without fission) in most nuclear fuels such as plutonium-239, making epithermal-spectrum reactors using these fuels less desirable, as captures not only waste the one neutron captured but also usually result in a nuclide that is not fissile with thermal or epithermal neutrons, though still fissionable with fast neutrons. The exception is uranium-233 of the thorium cycle, which has good capture-fission ratios at all neutron energies.

High-energy neutrons have much more energy than fission energy neutrons and are generated as secondary particles by particle accelerators or in the atmosphere from cosmic rays. These high-energy neutrons are extremely efficient at ionization and far more likely to cause cell death than X-rays or protons.[90][91]

^ abcGlasstone, Samuel; Dolan, Philip J., eds. (1977), The Effects of Nuclear Weapons (3rd ed.), U.S. Dept. of Defense and Energy Research and Development Administration, U.S. Government Printing Office, ISBN978-1-60322-016-3

^ abcNakamura, K (2010). "Review of Particle Physics". Journal of Physics G. 37 (7A): 075021. Bibcode:2010JPhG...37g5021N. doi:10.1088/0954-3899/37/7A/075021.PDF with 2011 partial update for the 2012 edition
The exact value of the mean lifetime is still uncertain, due to conflicting results from experiments.
The Particle Data Group reports values up to six seconds apart (more than four standard deviations), commenting that "our 2006, 2008, and 2010 Reviews stayed with 885.7±0.8 s; but we noted that in light of SEREBROV 05 our value should be regarded as suspect until further experiments clarified matters. Since our 2010 Review, PICHLMAIER 10 has obtained a mean life of 880.7±1.8 s, closer to the value of SEREBROV 05 than to our average. And SEREBROV 10B[...] claims their values should be lowered by about 6 s, which would bring them into line with the two lower values. However, those reevaluations have not received an enthusiastic response from the experimenters in question; and in any case the Particle Data Group would have to await published changes (by those experimenters) of published values.
At this point, we can think of nothing better to do than to average the seven best but discordant measurements, getting 881.5±1.5s. Note that the error includes a scale factor of 2.7. This is a jump of 4.2 old (and 2.8 new) standard deviations. This state of affairs is a particularly unhappy one, because the value is so important. We again call upon the experimenters to clear this up."